Felicia is deciding on her schedule for next semester. She must take each of the following classes: English 102, Spanish 102, History 102, and College Algebra. If there are 15 sections of English 102, 9 sections of Spanish 102, 12 sections of History 102, and 13 sections of College Algebra, how many different possible schedules are there for Felicia to choose from? Assume there are no time conflicts between the different classes.

The algebraic expression can be simplified to 4p√2q³r

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

The expression can be simplified as follow:

2√(8p²q³r) = 2 * √8 * √p² √(q³r)

                  = 2 * √(4 * 2) * p √(q³r)

                  = 2 * √4 * √2 * p √(q³r)

                  = 2 * 2 * √2 * p √(q³r)

                  = 4p√2q³r

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Question in English

Could you help me solve this? I have the answer what I need is the procedure. Thank you so much

2√8p²q³r

Answer:160/30000 simplified would be 2/375

Step-by-step explanation:

Exact Form:

[tex]\frac{2}{375}[/tex]

Decimal Form:

0.0053

The y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).

The y-intercept is the point where a function or a curve intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

The y-intercept of a function is the point where the graph of the function intersects the y-axis. To find the y-intercept of the function F(x) = 2(x - 7)(x - 3), we need to substitute 0 for x in the equation:

F(x) = 2(x - 7)(x - 3)

So, we have:

F(0) = 2(0 - 7)(0 - 3)

Simplifying this expression, we get:

F(0) = 2(-7)(-3)

F(0) = 42

Therefore, the y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).

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Answer:

-|x|+1

Step-by-step explanation:

Based on the given frequency distribution, the estimated mean carrying load of the beams tested is approximately 904.2 pounds per square foot.

To estimate the mean carrying load of the beams tested, we need to find the weighted average of the midpoints of each data class.

First, we need to find the midpoint of each class interval. We can do this by taking the average of the lower and upper limits of each interval:

Midpoint of 860 to 879 = (860 + 879) / 2 = 869.5

Midpoint of 880 to 899 = (880 + 899) / 2 = 889.5

Midpoint of 900 to 919 = (900 + 919) / 2 = 909.5

Midpoint of 920 to 939 = (920 + 939) / 2 = 929.5

Midpoint of 940 to 959 = (940 + 959) / 2 = 949.5

Next, we can find the weighted average of these midpoints, using the frequencies as weights. We can set up a table to organize our calculations:

Data class Midpoint Frequency Midpoint x Frequency

860-879           869.5                5                  4,347.5

880-899           889.5         9                         8,005.5

900-919           909.5         12                        10,914

920-939           929.5          6                         5,577

940-959            949.5          2                          1,899

Total                          34                       30,743.5

To find the weighted average, we divide the sum of the products in the last column by the total frequency:

Weighted average = Sum of (Midpoint x Frequency) / Total frequency

Weighted average = 30,743.5 / 34

Weighted average ≈ 904.2

Therefore, based on the given frequency distribution, the estimated mean carrying load of the beams tested is approximately 904.2 pounds per square foot.

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Answer:

x = (y-z)/3

Step-by-step explanation:

z = 3x + y

3x = z - y

x = (z - y)/3

The two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.

Since the two buses are traveling towards each other at constant speeds, we can use the formula for finding the time two objects meet when traveling at constant speeds in opposite directions:

t = (d2 - d1)/(v1 + v2)

Where t is the time they meet, d1 is the distance the first bus travels, d2 is the distance the second bus travels, v1 is the speed of the first bus, and v2 is the speed of the second bus.

In this case, d1 is the distance between NY and Boston (approx. 200 miles), d2 is the distance between Boston and NY (also approx. 200 miles), v1 is the speed of the first bus (200 miles in 5 hours, or 40 miles/hour), and v2 is the speed of the second bus (200 miles in 5 hours, or 40 miles/hour).

Plugging these values into the formula, we get:

t = (200 - 200)/(40 + 40)

t = 0/80

t = 0

Hence, the two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.

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The measurement of angle Y which is a twin angle will be equal to 116 degrees which is option A.

What is an Isosceles Triangle?

The triangle which has any two sides equal in length is called as Isosceles Triangles. Also the two angles which is opposite to the equal sides are equal and third angle is unequal. The unequal side which is present is called the base of the triangle. Measurement of the altitude can be done from base to the vertex (which is topmost) of the triangle.

Here, the value of angle X is given 32 degree.

Therefore the value of angle Z will also be 32 degree (due to the property of isosceles triangle)

By angle sum property:

X+Y+Z=180

32+Y+32=180

Therefore, Y = 116 degree

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Answer:

Step-by-step explanation:

Start by finding the slope of the line that passes through both the 12 roses bouquet and the 18 roses bouquet.

point 1: (12,61)

point 2: (18,79)

m=y^2-y^1/x^2-x^1

m=79-61/18-12

m=18/6

m=3

then, using one of the points find the fixed costs

P=m*r+b

using 12,61

61=3*12+b

61-36=b

b=25

Answer:

The general equation that represents the linear relationship is:

P=25+3r

Answer:

A tangent is a line that touches the curve or a circle at a point..

Answer:

254.34

Step-by-step explanation:

πr^2

3.14*81

254.34

The p-value method yields P (T > 2.119) = 0.0359. It may be said that, at a 1% level of significance, there has been no decline in crime since the program's inception.

The observations for the paired t-test are drawn from a single random pair sample. There are the same number of observations in both samples. Each respondent has two observations for the experimental variable recorded.

The alternative is:

[tex]H_{0} =[/tex]: Since the program's launch, there has been no drop in the number of crimes.

The alternate theory is that:

[tex]H_{a} =[/tex] Since the start of the programme, fewer crimes have been committed.

Mathematically,

[tex]H_{0} =[/tex] μo = 0

[tex]H_{a} =[/tex] μd > 0

Given table:

Number of Crimes   Before   After   d = (before - after)    d²

A                                  14           2          14-2 =  12              14² = 144                                

B                                  7            7           17 - 7 =  0              0² = 0

C                                  4            3           4 - 3 =  1                 1² = 1

D                                  5            6           5 - 6 = -1              -1² = 1

E                                  17            8          17-8 =  9                 9² = 81
F                                  12           13          12 - 13 = -1             -1² = 1
G                                 8              3          8 - 3=  5              5² = 25
H                                 9              5          9 -5 =  4              4² = 16

Total                           8                             29                        269

The formula for the t statistic is:

t = ∑d / √[n(∑d²) - (∑d)²] / (n - 1)

t = 29 / √[8*269 - 29²] / (8 - 1)

t = 2.119

As a result, the test statistic's value is 2.119.

The p-value is inconsequential since it exceeds the specified significance level of 0.01 in this case.

This indicates that at a 1% level of significance, the null hypothesis cannot be ruled out.

As a result, it may be said that, at a 1% level of significance, there has been no crime decline in since the program's inception.

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The slope of the line which passes through points (-2, 1) and (0, -3) is calculated as: m = -2.

In order to find the slope of the line given in the graph, pick two points on the line, then plug in their coordinates into the slope formula given as:

Slope (m) = change in y / change in x = y2 - y1 / x2 - x1

We have:

(-2, 1) = (x1, y1)

(0, -3) = (x2, y2)

Plug in the values:

Slope (m) = (-3 - 1) / (0 - (-2))

m = -4 / 2

Slope of the line (m) = -2

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The slope of the line represented by the graph is equal to -2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (-3 - 3)/(0 + 3)

Slope (m) = (-6)/(3)

Slope (m) = -2.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to -2.

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The slope of the line which passes through points (-2, 1) and (0, -3) is calculated as: m = -2.

In order to find the slope of the line given in the graph, pick two points on the line, then plug in their coordinates into the slope formula given as:

Slope (m) = change in y / change in x = y2 - y1 / x2 - x1

We have:

(-2, 1) = (x1, y1)

(0, -3) = (x2, y2)

Plug in the values:

Slope (m) = (-3 - 1) / (0 - (-2))

m = -4 / 2

Slope of the line (m) = -2

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The slope of the line represented by the graph is equal to -2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (-3 - 3)/(0 + 3)

Slope (m) = (-6)/(3)

Slope (m) = -2.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to -2.

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Answer:

1.75 inches (pls give brainliest lol!)

Step-by-step explanation:

Let's use a proportion to solve the problem:

On the first map, 2.8 inches represents 25 miles:

2.8 / 1 = 25 / x

Simplifying the equation, we get:

x = 25(2.8)/1 = 70

Therefore, the distance between the two cities in the first map is 70 miles.

Now, let's find the distance between the same two cities on the second map, which has a scale of 1 inch to 40 miles:

We want to find how many inches on the second map represent 70 miles. Let's call this value y.

1 / 40 = y / 70

Solving for y, we get:

y = 70/40 = 1.75

Therefore, the two cities would be 1.75 inches apart on the second map with the 1 inch to 40 miles scale.

Based on the information provided in the question, we can conclude that the histogram represents 20 math team members.

[tex]\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]

♥️ [tex]{\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\[/tex]

The values of y and z that make the triangles to be congruent are 13 each

From the question, we have the following parameters that can be used in our computation:

The triangles

For the two triangles to be congruent, the following equations must be true

2y = y + 13

y + 5z - 20 =  2y + z + 19

When the above equations are evaluated, we have

y = 13

Next, we have

4z = y + 39

So, we have

4z = 13 + 39

Add and divide by 4

z = 13

Hence, the values of y and z are 13

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The number that could represent point Q is to be considered as the option c.  2 1/2.

Calculation of the number:

Since

p = -4

q could be 6.5 units to the right or to the left of point p.

So, to the right, it should be like

=p + q

= -4 +  6.5

= 2.5

Hence, The number that could represent point Q is to be considered as option c.  2 1/2.

In mathematics, a tool known as a number line offers a graphical representation of numerical values arranged in sequential order from left to right with zero located in the center. This instrument is frequently applied throughout mathematical fields when interpreting negative and positive numbers along with fractions and decimals.

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Answer:the upper right one( the dash line that hit -2

Step-by-step explanation:

Okay, let's solve this step-by-step:

3.25x×400=2.50x+600

1300x = 1500

x = 500

So when x = 500, the costs are equal.

The zeros of f according to their multiplicity are:

Zero of multiplicity 1: x = -8, x = -3, x = 0, x = 9

Zero of multiplicity 2: None

Zero of multiplicity 3: None

Here,

We have,

The zeros of a polynomial function are the values of x that make the function equal to zero. The multiplicity of a zero is the number of times it appears as a factor in the polynomial.

In the given function f(x), the zeros are the values of x that make the function equal to zero.

We can find these values by setting the function equal to zero and solving for x.

f(x) = 7x(x-9)(x+8)^2(x+3) = 0

Therefore, the zeros of f(x) are x = -8, x = -3, x = 0, and x = 9.

To determine the multiplicity of each zero, we can look at the degree to which the corresponding factor appears in the polynomial.

For example, x = -8 is a zero of multiplicity 2 because it appears as a factor twice in the function, as (x+8)^2.

Similarly, x = -3, x = 0, and x = 9 are zeros of multiplicity 1 because they each appear as a factor once in the function.

There are no zeros of multiplicity 3 or higher in this function, so we can list "None" for those categories.

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He completed volunteering in 39 hours 40 minutes in 4 weeks

How to determine this

If Ken volunteers 1 hr 25 mins each day

i.e 1 hr 25 mins = 1 days

By converting 1 hr 25 mins to mins

When 60 mins = 1 hr

1 hr 25 mins = 60 + 25 = 85 mins

How many hours of volunteering is completed in 4 weeks

Let x represent the numbers of hours

i.e x = 4 weeks

By converting 4 weeks to days

When 7 days = 1 week

4 weeks = 4 * 7 days

= 28 days

So, when 85 mins = 1 day

x mins = 28 days

x = 28 days * 85 mins/1 day

x = 2380 mins

By converting it back to hour

When 60 mins = 1 hour

2380 mins = x

x = 2380/60 hour

x = 39 hours 40 mins

Therefore, the hours that can be completed in 4 weeks is 39 hours 40 minutes

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Answer:

average rate of change = 12

Step-by-step explanation:

the average rate of change of f(x) in the interval a ≤ x ≤ b is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here the interval is 2 ≤ x ≤ 4 , then

f(b) = f(4) = 2(4)² - 2 = 2(16) - 2 = 32 - 2 = 30

f(a) = 2(2)² - 2 = 2(4) - 2 = 8 - 2 = 6

then

average rate of change = [tex]\frac{30-6}{4-2}[/tex] = [tex]\frac{24}{2}[/tex] = 12

Answer:

3) The graph that has three x-intercepts

9) Plot the points on the graphing calculator, and then generate a linear regression equation. That equation is:

y = 2.857x - 1.4286

The closest equation is y = 3x - 2. That equation best represents the regression line for this data.

That this is just an estimate of the true proportion of all voters who would vote for Brown, based on the sample of 350 voters surveyed. The true proportion could be different, due to sampling variability.

What is Statistic?

A statistic is a numerical measure that summarizes some aspect of a dataset. It is a way to describe a sample of data in a concise and meaningful way. Common examples of statistics include measures of central tendency such as the mean, median, and mode, as well as measures of variability such as the range, standard deviation, and variance.

The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is the sample proportion, which is the number of voters who said they'd vote for Brown divided by the total number of voters surveyed:

Number of votes who said they'd vote for brown

    total number of surveyed

= 109/350

=0.31

Therefore, based on the sample of 350 voters surveyed.

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The coefficient of determination is: 88%

The following table shows the calculations:

X Y X^2 Y^2 XY

22 3 484 9 66

17 4 289 16 68

41 21 1681 441 861

5 1 25 1 5

36 16 1296 256 576

19 7 361 49 133

24 14 576 196 336

6 4 36 16 24

8 2 64 4 16

52 32 2704 1024 1664

35 23 1225 529 805

Total 265 127 8741 2541 4554

Sample size: n=11

Now,

(a)

The coefficient of correlation is :

r=[tex]\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=0.94[/tex]

(b)

The slope of the regression equation is 0.63

S.

and intercept of the equation will be

[tex]b_{0}=\frac{1}{n}(\sum y - b_{1} \sum x)=-3.729965\approx -3.73[/tex]

So the regression equation will be

y'=-3.73+0.63*x

(c)

The coefficient of determination is: 88%

Regression is a statistical analytical method that investigates correlations between two or more variables. Its widespread usage stems from its ability to forecast or assess the value of one contingent variable using one or many independently varying variables.

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The break even sales for the current year using the contribution per unit  is 5.27.

The formula to find the break even sales is,

Break even sales = Fixed costs / Contribution per unit

Now,

Contribution per unit = Sales price per unit - Variable cost per unit.

Sales price = $6,512

Variable cost = (75% × cost of goods sold) + (50% × marketing, general and administration expenses)

                      = (75% × $1,628) + (50% × $592)

                      = $1517

Contribution margin = $6,512 - $1517 = $4995

Contribution per unit = $4995 / 37 = $135 per million

Fixed costs = (25% × cost of goods sold) + (50% × marketing, general and administration expenses)

                   = $703

Break even sales = 703 / 135 = 5.21

Hence the break even sales is 5.27.

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To find the angle of depression, we can use the tangent function in trigonometry. In this situation, we have a right triangle where the height (opposite side) is 400 feet, and the distance (adjacent side) is 18,410 feet.

tan(angle) = opposite / adjacent

tan(angle) = 400 / 18,410

Now, we'll use the arctangent (inverse tangent) function to find the angle:

angle = arctan(400 / 18,410)

angle ≈ 1.25 degrees

The angle of depression from the top of the lighthouse to the waterline of the ship is approximately 1.25 degrees, rounded to the nearest hundredth of a degree.

Answer:

1 over 3 would juts be 1/3

Answer:

[tex]x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} [/tex]

To find the missing angle measure, we need to use the fact that the sum of angles in a triangle is 180 degrees. Let's denote the missing angle as x. We know that one angle is 38 degrees and another angle is 12.5 degrees.Therefore, the missing angle measure is 129.5 degrees.

By subtracting these two angles from 180 degrees, we get:

180 - 38 - 12.5 = 129.5

Without additional information, it is not possible to determine the remaining parts of the triangle. We would need the lengths of at least one side or the measures of other angles to solve for the missing parts.

The given information states that AC is equal to AB minus mzB. Without knowing the values of AB and mzB, we cannot determine the exact length of AC. We would need additional information to solve for the length of AC.Therefore, the missing angle measure is 129.5 degrees.

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